There are so many elements I've built that it's hard to begin.
Suffice it to say, this is the induction of nth reusable and throwaway designed geometric AI. They are modular, train fast, can be tasked to transform rapidly, and are inherently high - high accuracy.
They are tiny. Very tiny.
They are a fraction of the size of the big model and outperform them.
They can house 100 classifiers in a single 72kb space using the geometric vocab.
https://huggingface.co/datasets/AbstractPhil/geometric-vocab-32d
There are multiple working notebooks and proofs that showcase this potential. They achieve 99.95% on standard mnist and handle cifar100 at >+20% accuracy than the features extracted from clips in conjunction with the pentachoron classifiers.
The formulas are complex, but are genuinely capable and scalable upward.
https://github.com/AbstractEyes/lattice_vocabulary/blob/master/symbolic_lattice_formula_map.md
What is a pentachoron?
Simply put; a 5d triangle. The solution's manifestation came from Cayley Menger simplex formulas, and Nikola Tesla's obsession with the 3 6 9 system.
I discovered, that this isn't actually... correct. It's close, and a stepping off point - but flawed. I got very little ground from just using the 3 6 9 system. I found that using triplets was a good start, however the rule of threes requires... more.
It requires a systemic overarching force, a kind of... guide. Something that says what is what and why is why and where is where and when is when... etc.
Who, what, when, where, why - didn't form from coincidence. I have deterministic geometric capacity that binds unicode directly to our words, and the very nature of the distances being preserved, curates the naturalistic responses that these geometries diverge autonomously by curated trajectory.
In other words, the map is in front of us - and it's in everything, but it's nothing so simple as... a 3 6 9 paradigm.
5d isn't what... people say 5d is.
It's not some sort of map of everything. It's not... 5d like people say it is. It's not something that one can simply have all the answers to, as quantum physicists would imply - this is not practical and the formulas in quantum physics provides almost no yield.
In fact, I'd say I wasted more time on them than actually getting use from them. They are impractical and they are incoherent more often than useful. That is not 5d, that is some sort of... guess-all math, and it's not 6d either. It's like trying to predict impossible predictions, and using flawed math to do it.
Euler math fits with Pentachoron
The system is conformant and the math aligns. The multitude of structures overlap, and the systems can be used in conjunction; meaning the linear architectures can communicate with the geometric architectures. The geometric architectures learn faster and maintain cohesion; designed specifically to cook fast - usually within a few epochs.
This enables fun... elements with this system. Such as...
Geometric Diffusion
Euler-Discreet Flow-Matching IS applied in multiple notebooks. The math is still a bit imperfect, but the outcome yields that it's very possible to regenerate the very vocabulary itself using images.
Simultaneously you can diffuse those same images from the geometry. In other words, the future of diffusion is... Tiny. Very tiny in fact.
The outcome shows that these diffusion models are less than 20 megs and produce 100 classes of images; with cfg control, overlap, shift, and a multitude of other elements that diffusion are capable of doing usually... with the added benefit of quite literally generating the geometry for classification FROM THE SAME MODEL.
Diffusion and classification aren't it.
Early showcasing shows that it can be used to supplement bert outputs; which many VIT and CLIP-VIT models are based on. This means... yes. You can in fact create entire classifiers with it, and the accuracy from the miniature (sub 20 meg encoders with little training show) you can in fact train high accuracy throw-away heads within a near immediate time span.
Beeper - the geometric LLM
Yes, there is a geometric LLM but beeper is imperfect - she requires a full remake from the ground up, as this version was flawed and was not trained using the pentachora vocabulary but instead I used raw unicode.
https://huggingface.co/AbstractPhil/beeper-rose-v4
5d pentachora vocabulary with... Unicode. Yes, unicode.
Wordnet helps yes, and it will continue to help. It allows the system to conform the unicode into a more robust definition driven format. Automatically combining the elements into subsequently potent pentachoron geometric shapes.
These are formed using a series of formulas - preserving the triadic, orthogonal, and additional elements to allow these systems to perfectly align along multiple geometric planes.
Bullshit.
Below are MULTIPLE notebooks, each runnable standalone and proving everything I explained here.
1 of 7 notebooks; frequency based dual band encoding
This system is similar to the multi-channel frequency encoder, but it's specialized in greyscale.
https://huggingface.co/AbstractPhil/pentachora-greyscale-frequency-encoded
2 of 7 notebooks; multi-frequency colored encoding.
A small encoder meant to house multiple image frequencies to map directly into the pentachora schema.
https://huggingface.co/AbstractPhil/pentachora-multi-channel-frequency-encoded
3 of 7 notebooks; reserved for paper, some earlier weights released
Specifically terrible with cifar100, notebook 5 however is not. This version is quite inaccurate, however the weights are released nonetheless. This is on the menu for the bulk train so we can all see the outcomes of the h100 testing.
https://huggingface.co/AbstractPhil/geometric-diffusion-cifar100
3 4 and 5 are preserved for the official papers and the ablation study.
4 of 7 is geometric distillation using teacher/student paradigms
specifically meant to curate constellations of multi-dispatch capable experts along the finite spectrum.
bidirectional diffusion prototype
5 of 7 is a mobius strip system
built specifically with infinite corridors lined with resonant pathway pentachora; thousands. Each helix-based using many many formulas. Apparently, too many as the accuracy suffered. It was a fantastic experiment however and it showcases many elements.
diffusion variation, classification variation, and llm variation
6 of 7 is a released notebook
A multi-spectrum baseline system built specifically to handle clip inputs and produce geometric capability using the new vocabulary as a test basin. It was using standard learning protocols and paradigms, and it showed that each train improved the parent model's coherence rather than damaging it... In a fraction of the size. Sometimes less than 100 kb in size.
https://huggingface.co/AbstractPhil/geoclip-vit-large-patch14-unicode-256dx1024d
https://huggingface.co/AbstractPhil/geoclip-vit-large-patch14-unicode-64x64d
https://huggingface.co/AbstractPhil/geoclip-vit-large-patch14-unicode-768x768d
https://huggingface.co/AbstractPhil/geoclip-rose-vit-l-14-uni-32dx32d
This one was kind of hard to track down the notebook for, so here it is.
the 7th of 7 notebooks;
A manufacturing notebook for training param testing using the rose-loss accented trajectory assessment curation - rose magnitude loss. Which handles triplets in conjunction with the five pentachoron controller segments utilizing the geometric vocab. These are trained using clip features and are each labeled better and within a proper.